T-tests

Question 1

What is NHST?

Answer 1

• “a method of statistical inference by which an experimental factor is tested against a hypothesis of no effect or no relationship (i.e., null hypothesis) based on a given observation”
• Testing the probability of getting 2 sample means (from different conditions) that are at least this different IF they were actually drawn from populations with the same mean.

Question 2

What is a sampling distribution? How do we use it in NHST?

Answer 2

• a theoretical distribution of infinitely many samples that represents the null hypothesis
• provides an expected value for null (0)
• look at the obtained stat in relation to the sampling distribution to determine how extreme the sample stat is & to calculate t-stat & p-value

Question 3

What is a p-value? (describe what it means conceptually)

Answer 3

• The probability of observing a result at least as extreme as a test statistic (e.g. t value), assuming the null hypothesis of no effect is true

Question 4

What’s the rule for how to use a p-value to determine if there is a statistically significant effect?

Answer 4

• If p<alpha, you can reject the null hypothesis and conclude that there is a statistically significant effect of the IV on the DV. (Usually if p<0.05)

Question 5

What does “statistically significant” mean?

Answer 5

• there is a real difference between two conditions

Question 6

What is the sample distribution?

Answer 6

• distribution of a subset (sample) of a population

ie data points collected from your experiment

Question 7

What is the population distribution?

Answer 7

• distribution of all data points in the population

Question 8

What is the sampling distribution?

Answer 8

• distribution of infinitely many samples
• Distribution of a statistic from your sample

specific statistic –> mu diff bar –> expected value for sample mean differences

Question 9

Symbols for mean & standard deviation for a pop, sample, & sampling distribution?

Answer 9

Pop: μ, ŝ / σ
Sample: x̄, SD
Sampling: μ-diff bar, ŝ-diff bar

Question 10

What is df? How are they calculated? How are they used in NHST?

Answer 10

• describes the t-distribution that we use for the t-test
• based on sample size
• n-1 for each sample group

Question 11

What is the t-distribution? How is it related to df & normal dist?

Answer 11

• a mathematical distribution that describes the standardized distances of sample means to the population mean
• shape determined by df
  → df larger = t-dist. ~ normal
  → df small = flatter, tails bigger

Question 12

How do you use the t-distribution in NHST?

Answer 12

• determine where the obtained stat fits within the t-dist, relative to all other possible scores for that stat IF the null hyp. were true
• Then, you can determine the probability of obtaining a stat at least that extreme given the null

Question 13

T-stat equation?

Answer 13

       ŝ-diff

Question 14

Type 1 error? What happens?

Answer 14

• false alarm
• REJECT the null
• conclude that there IS a real difference
• irl there is NO real difference

Question 15

Type 2 error? What happens?

Answer 15

• miss
• FAIL to reject the null
• conclude there is NO real difference
• irl there IS a real difference